AcaWiki:Top 100 Papers

We are driving towards gathering summaries of the Top 100 academic papers in the world. This is a large effort to increase the number of our papers, get more students, more researchers, and academics to know about the project and share their specific knowledge. We need your specific expertise to make this project sucessful.

In just 36 pages, Turing formulates (but does not name) the Turing Machine, recasts Gödel's famous First Incompleteness Theorem in terms of computation, describes the concept of universality, and in the appendix shows that computability by Turing machines is equivalent to computability by λ-definable functions (as studied by Church and Kleene).

It also represents the kind of paper I wish there were more of. It exposes the inspiration and thought processing behind a nest of ideas without the rigorous but limiting tone of a research paper. It is a shame that researchers have to wait for an opportunity like the ACM Turing Award to be able to express themselves in this mode. Of course, few researchers can write like John Backus. This papers clarity of vision amazes me.

One professor called it "the basis for truly 21st century mathematics." It is also reportedly accessible by beginning graduate students with some exposure to differential geometry and suitable for independent study or as a reading course. It is a 93 page paper and develops a lot of fundamental constructions and ideas from scratch. Here is Martin Guest's review on MathSciNet. -Justin Kerry at cc-by-sa attribution

For about 5 years I carried my copy with me everywhere I went, in an increasingly decrepit 3-ring binder weighed down by page after page of my own notes and explanations. One day, at a conference, a dispute arose over whether the main result of the paper held with integral coefficients or required one to work over the rationals. In the flash of an eye, four or five of us pulled out our copies and opened to the relevant page. Luckily, I was right: integral coefficients. The first time I left home without the paper, it felt like a rite of passage. Or at least that's the way I remember it. – Dan Ramras at cc-by-sa attribution

On formally undecidable propositions of Principia Mathematica and related systems

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Quantum Mechanical Computers

He introduces the idea of quantum computation, describes quantum circuits, explains how classical circuits can be simulated by quantum circuits, and shows how quantum circuits can compute functions without lots of garbage qubits (using uncomputation).

He then shows how any classical circuit can be encoded into a time-independent Hamiltonian! His proof goes through for quantum circuits too, therefore showing that time evolving Hamiltonians is BQP-hard! His Hamiltonian construction is also used in the proof of the quantum version of the Cook-Levin theorem, proved by Kitaev, which shows that k-local Hamiltonian is QMA-complete. cc-by-sa attribution

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Psychology

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Jonathan Haidt said "so important that the abstracts... should be posted in psychology departments all over the country." and that “the article is one of my favorite papers of the last ten years. I believe that they have solved one of the most important and longstanding puzzles in psychology: why are we so good at reasoning in some cases, but so hopelessly biased in others?

Milgram, S. (1974). Obedience to Authority. New York: Harper and Row. See Wikipedia

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Sociology

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Sociology Papers

Sociology is a big field with many branches (e.g. network research, health communication, media effects, organizational communication, classical sociology, etc.). Perhaps it would be better to make top 5's for each?